How to Divide Whole Numbers by Fractions - A Simple Guide
In this guide to dividing whole numbers by fractions, you'll find kid-friendly explanations, solved examples, and practice questions to test your skills!
Imagine you have a pizza sliced into 8 equal pieces, and you’re sharing it with 4 friends. Each person gets 2 slices, right? We can figure this out by dividing the total slices by the number of friends: 8 ÷ 4 = 2.
Using fractions, we can say each person’s share is \( \Large \frac{2}{8}\). But guess what? \( \Large \frac{2}{8}\) is the same as \( \Large \frac{1}{4}\)!
Even though the numbers look different, they represent the exact same amount of pizza. That’s what we call equivalent fractions!
By the end of this guide, you’ll understand how equivalent fractions work and why they’re so useful. Let’s dive in!
Equivalent fractions are fractions that represent the same part of a whole, even though they have different numerators (top numbers) and denominators (bottom numbers). This means that the value of the fractions is the same, even if the numbers look different.
Let’s return to our pizza example.
To get evenly sized slices, you probably started to cut your pizza into 4 big parts.
Then you probably sliced it diagonally, halving each of the four slices to get a total of 8:
When you compare the quarter slices (\( \Large \frac{1}{4}\)) with the 2 eighths slices (\( \Large \frac{2}{8}\)), notice how they are equal in size?
That is why we say that fractions like \( \Large \frac{1}{4}\) and \( \Large \frac{2}{8}\) are equivalent.
To find out if fractions are equivalent, all we have to do is either multiply or divide both the numerator and denominator by the same number.
To use the multiplication method, simply multiply both the numerator (the top number) and the denominator (the bottom number) of a fraction by the same number.
Multiplying the numerator and denominator by the same number keeps the fraction’s value the same, even though our numbers will change.
Let’s see it in action using the fraction \( \Large \frac{2}{3}\)
To keep things simple, we’ll multiply it by a small number – number 2.
\( \Large \frac{2×2}{3×2}\) = \( \Large \frac{4}{6}\)
Conclusion: \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\) are equivalent numbers.
We can even check this by dividing 2 ÷ 3 and 4 ÷ 6 to compare the results.
2 ÷ 3 = 0.66
4 ÷ 6 = 0.66
Finding equivalent fractions using the division method involves dividing both the numerator and the denominator of a fraction by the same number.
This works only if the numerator and denominator share a common factor which is a number that divides both evenly.
By dividing, we simplify the fraction into a smaller, equivalent form that represents the same value.
Let’s try this with \( \Large \frac{8}{12}\).
To find a common factor, we look for a number that divides both 8 and 12 evenly, such as the numbers 2 and 4. Their greatest common factor (GCF) is 4, so let’s start with that one.
We’ll then divide the numerator and denominator by the GCF:
\( \Large \frac{8 ÷ 4}{12 ÷ 4}\) = \( \Large \frac{2}{3}\)
So, \( \Large \frac{8}{12}\) is equivalent to \( \Large \frac{2}{3}\).
Now, let’s try the other common factor of 8 and 12 which is 2.
\( \Large \frac{8 ÷ 2}{12 ÷ 2}\) = \( \Large \frac{4}{6}\)
So, \( \Large \frac{8}{12}\) is also equivalent to \( \Large \frac{4}{6}\).
How about \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\)?
You guessed it! \( \Large \frac{2}{3}\) and \( \Large \frac{4}{6}\) are also equivalent fractions as \( \Large \frac{4}{6}\) can be further simplified into \( \Large \frac{2}{3}\).
Brush up on how to find the greatest common factor:
Understanding equivalent fractions isn’t just about doing well in math class—it’s a skill you’ll use in many real-world situations!
Let’s return to the first example we talked about. You might notice that \( \Large \frac{1}{4}\) of the pizza for each person is the same as \( \Large \frac{2}{8}\), especially if the pizza is already cut into 8 slices.
Using equivalent fractions ensures everyone gets their fair share—no arguments needed!
Most recipes come with specific measurements. To add ingredients properly, you might need to use equivalent fractions.
For example, you need \( \Large \frac{1}{2}\) cup of sugar for your cake, but your measuring cup only has a \( \Large \frac{2}{4}\) mark.
When you know that they are the same thing, you will not need to worry about messing up a recipe.
While shopping, you might see two packs of juice boxes. One pack says it costs $6 for 12 boxes, and another is $3 for 6 boxes.
Are these deals the same?
Using equivalent fractions, you can see that $6/12 simplifies to $3/6, so both packs cost the same per box. This math trick can help you save money!
1. True or False:
\( \Large \frac{1}{2}\) is the same as \( \Large \frac{2}{4}\)?
2. Which Fraction is Equivalent to 3/6?
3. Fill in the blank
If \( \Large \frac{4}{8}\) = \( \Large \frac{1}{x}\), what is x?
4. True of False:
Sam says that \( \Large \frac{5}{10}\) is an equivalent fraction of \( \Large \frac{1}{2}\). Is he correct?
Although fractions are introduced in grades 1-2, they are formally taught in the 3rd grade.
Equivalent fractions are a foundational concept that helps students understand more advanced math topics. They provide a way to see relationships between numbers and simplify calculations, making them essential in many areas of math.
Equivalent fractions help us compare, simplify, and perform operations like addition and subtraction with fractions. They’re a foundational concept in understanding how fractions work and are useful in real-life scenarios, like dividing pizza slices or measuring ingredients in a recipe.
By practicing equivalent fractions, third graders can build a strong understanding of how fractions relate to each other and gain confidence in working with them.
Mathnasium of Allen’s specially trained math tutors work with elementary school students of all skill levels to help them understand and excel in any math class and topic, including equivalent fractions.
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